Monte Carlo Methods and Appl., Vol. 9, No. 2, pp. 167 { 188 (2003) c ® VSP 2003 Stochastic Lagrangian footprint calculations over a surface with an abrupt change of roughness height ¤ O. Kurbanmuradov 1 , A. Levykin 2 , U. Rannik 3 , K. Sabelfeld 2;4 and T. Vesala 3 1 Center for Phys. Math. Research, Turkmenian State University, Turkmenbashy av. 31, 744000 Ashgabad, Turkmenistan, 2 Institute of Comput. Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Lavrentieva str., 6 630090 Novosibirsk, Russia, 3 Department of Physics, FIN-00014 University of Helsinki, Finland, 4 Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D { 10117 Berlin, Germany E-mail: sabelfel@wias-berlin.de Abstract | Forward and backward stochastic Lagrangian trajectory simulation methods are developed to calculate the footprint and cumulative footprint functions of concentration and ®uxes in the case when the ground surface has an abrupt change of the roughness height. The statistical characteristics to the stochastic model are extracted numerically from a closure model we developed for the atmospheric boundary layer. The ®ux footprint function is perturbed in comparison with the footprint function for surface without change in properties. The pertur- bation depends on the observation level as well as roughness change and distance from the observation point. It is concluded that the footprint function for horizontally homogeneous sur- face, widely used in estimation of su¯cient fetch for measurements, can be seriously biased in many cases of practical importance. 1 Introduction Over a horizontally homogeneous surface the °ux measuered by micrometeorological tech- nique equals to the surface °ux. This principle is used to determine the surface exchange by the eddy covariance (EC) technique. The °ux footprint function (e.g. Schmid, 1994) links the surface emissions to the observed °uxes above surface at EC measurement level. The footprint function is therefore used to estimate a distance required to make reliable EC meaurements, i.e. if the horizontal extent of underlying surface of interest is su±- cient to determine its exchange rate. Extended tower measurements of °uxes over forests have been used during the last ten years to obtain detailed information on carbon and water exchanges between forest canopies and atmosphere. (Kaiser, 1998; Running, 1998; Valentini et al., 2000). Large areas of forest are not however common in Europe nor in ¤ Support by the European Grant INTAS-99-1501, the NATO Linkage Grant 978912 and Russian Foundation of the Basic Research (project 03-01-0091) is kindly acknowledged